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Geometry Mathley 16.2 collinear orthocenters

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June 14, 2020
geometryorthocentercollinear

Problem Statement

Let ABCDABCD be a quadrilateral and PP a point in the plane of the quadrilateral. Let M,NM,N be on the sides AC,BDAC,BD respectively such that PM∥BC,PN∥ADPM \parallel BC, PN \parallel AD. ACAC meets BDBD at EE. Prove that the orthocenter of triangles EBC,EAD,EMNEBC, EAD, EMN are collinear if and only if PP is on the line ABAB.
Đỗ Thanh Sơn
PS. Instead of the word collinear, it was written concurrent, probably a typo.
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